대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제39권3호
  • /
  • Pages.401-410
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  • 2002
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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GENERALIZED JENSEN'S FUNCTIONAL EQUATIONS AND APPROXIMATE ALGEBRA HOMOMORPHISMS

  • Bae, Jae-Hyeong (Department of Mathematics, Chungnam National University) ;
  • Park, Won-Gil (Department of Mathematics, Chungnam National University)
  • 발행 : 2002.08.01
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초록

We prove the generalized Hyers-Ulam-Rassias stability of generalized Jensen's functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with generalized Jensen's functional equations in Banach algebras.

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참고문헌

  1. On approximate ring homomorphisms R. Badora
  2. Complete Normed Algebras F. Bonsall;J. Duncan
  3. Duke Math. J. v.16 Approximately isometric and multiplicative transformations on continuous function rings D. G. Bourgin https://doi.org/10.1215/S0012-7094-49-01639-7
  4. Math. Scand. v.57 Means and convex combinations of unitary operators R. Kadison;G. Pedersen
  5. Aeq. Math. v.43 On Jensen's functional equation J. C. Parnami;H. L. Vasudeva https://doi.org/10.1007/BF01835703
  6. Proc. Amer. Math. Soc. v.72 On the stability of the linear mapping in Banach spaces Th. M. Rassias https://doi.org/10.1090/S0002-9939-1978-0507327-1

피인용 문헌

  1. On the stability of Euler–Lagrange type cubic mappings in quasi-Banach spaces vol.332, pp.2, 2007, https://doi.org/10.1016/j.jmaa.2006.11.024
  2. C *-Ternary 3-Homomorphisms on C *-Ternary Algebras vol.66, pp.1-2, 2014, https://doi.org/10.1007/s00025-014-0365-7
  3. A FIXED POINT APPROACH TO THE CAUCHY-RASSIAS STABILITY OF GENERAL JENSEN TYPE QUADRATIC-QUADRATIC MAPPINGS vol.47, pp.5, 2010, https://doi.org/10.4134/BKMS.2010.47.5.987
  4. Asymptotic behavior of the extended Jensen equation vol.46, pp.1, 2009, https://doi.org/10.1556/SScMath.2008.1077